Question 827668
{{{drawing(200,440,-5,25,-5,61,
line(-5,-5,25,25),
line(0,0,30,0),
locate(14.5,0,horizontal),locate(18,-1.8,line),
locate(18,18,hill),locate(18,16.2,slope),
triangle(0,0,14.14,0,14.14,52.78),
rectangle(14.14,0,13.14,1),
locate(14.64,2.3,P),locate(14.64,14.14,R),
locate(14.64,52.78,T),locate(0,0,S),
red(arrow(14.14,52.78,16.08,60)),
locate(16.5,60.5,to),locate(19.5,60.5,sun),
green(line(14.14,14.14,14.14,52.78)),locate(14.5,35,green(tree)),
locate(1.8,3.5,45^o),arc(0,0,12,12,-45,0),
locate(4,12,75^o),arc(0,0,20,20,-75,0)
)}}} RS = 20 m = shadow of tree
Consider right triangle RSP.
{{{PS=RS*cos(45^o)=(20m)(sqrt(2)/2)=14.14m}}} (rounded to nearest 0.1m)
{{{RP=RS*sin(45^o)=(20m)(sqrt(2)/2)=14.14m}}} (rounded to nearest 0.1m)
Consider right triangle TSP.
{{{PT=PS*tan(75^o)=(14.14m)*3.732=52.78m}}} (rounded to nearest 0.1m)
The height of the tree is
{{{RT=PT-RP=52.78m-14.14m=38.64m}}} (rounded to nearest 0.1m).
(Maybe it should be rounded to 39 meters, since the shadow's length and angles do not seem to have been measured with such fine precision).